Been trying for a few days to figure this out. Booted up my old computer which was in storage for a while. I had an old version of limewire that I had no trouble with. Decided to install newer version after old version wouldn't connect. Cannot connect. I'll answer following questions. THANKS!

1. OS version? (eg: Windows 98) XP
2. What firewalls you have? WINDOWS
3. How much ram? 71 GB
4. Hard Disk space available? 60.5
5. Connection type? (eg: dialup, broadband, cable, etc.) CABLE MODEM BROADBAND
6. Modem & router brand name & model numbers? SURFBOARD SB4100
7. Where are you trying to connect from (home, school, work, etc.)? HOME
8. What version of LimeWire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version. LIMEWIRE 4.14.8 JAVA1.5.0_02
9. Who is your ISP provider (Internet Service Provider)?GRANDECOM
10. Do this simple test for us. Using your browser go here: http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there? IT WORKS
11. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up. NO
12. Is this a your 1st try at LW or is this a new problem with an experienced user. NEW PROB
13. Do you see a brick wall in front of the blue world icon at the bottom of LW's interface? YES

Make sure that LW's being allowed thru the XP firewall. This link has some info.
User Cant Connect - LimeWire

Update your Java & try this version. Use the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Next, delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

Your modem doesn't have a firewall...do you have a router as well?

If none of that helps, follow foolofthehill's advice here for uninstalling LW & removing all traces of it.
http://www.gnutellaforums.com/283346-post2.html
Once you've done that, reinstall LW & make sure to use the offline installer. When you click to download LW & the download box pops up, cancel that. Now you'll see an option to download the offline installer
Lime Wire » Download LimeWire

Thanks, Birdy. I was messing with it all night trying little bits of advice I found and, low and behold, for some reason, it connected. I had added 2 ports as exceptions in my windows firewall and everytime I unchecked and rechecked udp or tcp it removed the brickwall from LW and my connection is all green. Maybe I didn't configure the liseting port correctly because I have to uncheck/check every time I run LW, but it works for me for now!